集体动力学中的四元数
Quaternions in collective dynamics
摘要：
我们引入了一个模型的多智能体动力学自组织运动，个人旅行在一个恒定的速度，同时试图通过他们的邻居的平均身体的态度。身体的态度表示通过酉四元数。我们证明了对应的模型在以前的工作中提出的三个第一作者的身体的态度表示的旋转矩阵。与以前的工作不同，这里介绍的基于个体的模型（IBM）是基于平行（而不是极）对齐的。从IBM出发，导出了动力学方程和宏观方程。这种方法的好处是双重的：首先，它允许更好地理解所获得的宏观方程，其次，这些方程易于进行数值研究，这是应用的关键。
英文摘要：
We introduce a model of multi-agent dynamics for self-organised motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbours. The body attitudes are represented through unitary quaternions. We prove the correspondance with the model presented in a previous work by the three first authors where the body attitudes are represented by rotation matrices. Differently from this previous work, the individual based model (IBM) introduced here is based on nematic (rather than polar) alignment. From the IBM, the kinetic and macroscopic equations are derived. The benefit of this approach is twofold: firstly, it allows for a better understanding of the macroscopic equations obtained and, secondly, these equations are prone to numerical studies, which is key for applications.
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